Learning-based Position and Stiffness Feedforward Control of Antagonistic Soft Pneumatic Actuators using Gaussian Processes

TL;DR

This paper tackles the challenge of simultaneously controlling the position $q$ and stiffness $s$ of antagonistic soft pneumatic actuators without relying on analytical models. It introduces a modular, 3D-printed VSA and trains two Gaussian process models to map the state $(q,s)$ to the actuator pressures $(p_1,p_2)$, forming a feedforward control that is supplemented by a small PI feedback on angle. The approach achieves an average feedforward error of $11.5\%$ of the total pressure range, and experiments show successful continuous adjustment of both position and stiffness across a range of configurations, demonstrating the method’s universality for VSAs. The work highlights the potential of GP-based learning for data-driven stiffness control in soft robotics, with implications for safer human-robot interaction and versatile manipulation in constrained environments.

Abstract

Variable stiffness actuator (VSA) designs are manifold. Conventional model-based control of these nonlinear systems is associated with high effort and design-dependent assumptions. In contrast, machine learning offers a promising alternative as models are trained on real measured data and nonlinearities are inherently taken into account. Our work presents a universal, learning-based approach for position and stiffness control of soft actuators. After introducing a soft pneumatic VSA, the model is learned with input-output data. For this purpose, a test bench was set up which enables automated measurement of the variable joint stiffness. During control, Gaussian processes are used to predict pressures for achieving desired position and stiffness. The feedforward error is on average 11.5% of the total pressure range and is compensated by feedback control. Experiments with the soft actuator show that the learning-based approach allows continuous adjustment of position and stiffness without model knowledge.

Figures (8)

• Figure 1: Soft pneumatic actuator for snake-robot applications: (a) Both continuous change of joint angle (upper two images) and increase of joint stiffness at constant position by antagonistic coactivation (lower two images) are possible. (b) The actuator is modular in terms of stackability. Three units exemplarily form an articulated soft robot with variable compliance.
• Figure 2: Soft actuator components: (a) The printed bellows consists of a soft membrane, a rigid platform for mounting and a sealing made of soft material. (b) Each actuator consists of two antagonistically acting bellows which are mounted on the upper and lower half of the frame with screws. The joint angle is measured with a Hall sensor. The printed tube connections are located inside the actuator.
• Figure 3: Block diagram of the proposed learning-based position and stiffness control of the soft actuator: The feedforward pressures $\boldsymbol{p}_\mathrm{FF}$ result from the Gaussian processes (\ref{['eq:desired_model']}) and are added to the target pressure difference from the feedback loop $\Delta p_\mathrm{FB}$ by means of (\ref{['eq:p_d']}).
• Figure 4: Test-bench architecture for measuring variable joint stiffness: Orange color represents communication elements such as sensor cables and blue color represents pneumatic components. The soft actuator with encoder is connected to the torque sensor and the motor via rigid connections.
• Figure 5: Automated measurement of joint stiffness at arbitrary steady-state angle $q_i$: (a) A trajectory is driven between $-1°{<}\tilde{q}_\mathrm{m}{=}q_\mathrm{m}{-}q_i{<}1°$. (b)--(c) During the two zero crossings in (a), the torques are recorded using torque sensor and two stiffness curves result. To obtain the stiffness measure $s_i$ for data point $i$, the average of the two slopes is calculated.